Extending Addition in Elliott′s Local Semigroup

Addition Behavior of a Numerical Semigroup 23

— In this work we study some objects describing the addition behavior of a numerical semigroup and we prove that they uniquely determine the numerical semigroup. We then study the case of Arf numerical semigroups and find some specific results. Résumé (Comportement de l’addition dans un semi-groupe numérique). — Dans ce travail, nous étudions des objets qui décrivent le comportement de l’additi...

Semigroup Product Formulas and Addition of Unbounded Operators

Bass Numbers of Semigroup-graded Local Cohomology

Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology H I(M) at any graded ideal I in terms of Ext modules. We use this method to obtain finiteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Q is simplicial, and a finitely g...

Semigroup presentations for test local groups

In this paper we exhibit a type of semigroup presentations which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety LG of all finite local groups and use them as test-semigroups to prove that LG and S, the pseudovariety of all finite semigroups, verify the same κ-identities involving κ-terms of rank at most 1, where κ denotes the implic...

Modulo quantifiers over functional vocabularies extending addition

We show that first order logic (FO) and first order logic extended with modulo counting quantifiers (FOMOD) over purely functional vocabularies which extend addition, satisfy the Crane beach property (CBP) if the logic satisfies a normal form (called positional normal form). This not only shows why logics over the addition vocabulary have the CBP but also gives new CBP results, for example for ...